Page 213 - Mechanics of Microelectromechanical Systems
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200 Chapter 4
where is the electric permittivity‚ is the overlap out-of-the-plane
dimension‚ is the initial gap in the x-direction‚ and x is the displacement
produced through attraction electrostatic forces. The initial-condition (no
actuation) capacitance can be found by taking x = 0 in Eq. (4.17)‚ namely:
As Eqs. (4.17) and (4.18) suggest‚ the variability in capacitance is only
produced through changing of the gap between the two plates because the
overlapped area is constant for a transverse electrostatic actuator.
When a voltage V is supplied externally‚ the electrostatic energy is:
The corresponding attraction force between the fixed and the mobile plates is
defined as the partial derivative of the electrostatic energy in terms of
displacement (which is similar to Castigliano’s displacement theorem)‚ and is
calculated by using Eqs. (4.18) and (4.19) as:
The initial force (when the two plates are apart) is:
Figure 4.23 Normalized force in terms of normalized displacement for a transverse
electrostatic actuator
By using the non-dimensional amounts:
